Question

Let’s say you have a Boolean rule/expression like so

(A OR B) AND (D OR E) AND F

You want to convert it into as many AND only expressions as possible, like so

A AND D AND F
A AND E AND F
B AND D AND F
B AND E AND F

You are just reducing the OR’s so it becomes

(A AND D AND F) OR (A AND E AND F) OR (...)

Is there a property in Boolean algebra that would do this?

Answer 1

Your example is exploiting the the distributivity of AND over OR, as shown here.

All you need to do is apply that successively. For example, using x*(y+z) = (x*y)+(x*z) (where * denotes AND and + denotes OR):

0. (A + B) * (D + E) * F
1. Apply to the first 2 brackets results in ((A+B)*D)+((A+B)*E)
2. Apply to content of each bracket results in (A*D+B*D)+(A*E+B*E)
3. So now you have ((A*D+B*D)+(A*E+B*E))*F
4. Applying the law again results in (A*D+B*D)*F+(A*E+B*E)*F
5. Apply one more time results in A*D*F+B*D*F+A*E*F+B*E*F, QED